Question

If x2 + y2 = 47xy then prove that 2log(x+y) = 2log7 + logx + logy .

Answer 1

Step-by-step explanation:

Given that,

x

2

+y

2

=47xy

Add 2xy both sides,

x

2

+y

2

+2xy=47xy+2xy

(x+y)

2

=49xy

Square root both sides,

x+y=7

xy

Substitute the above equation in,

log(

7

x+y

)=

2

1

(logx+logy)

log(

7

7

xy

)=

2

1

(logx+logy)

log(

7

7(xy)

2

1

)=

2

1

(logx+logy)

log((xy)

2

1

)=

2

1

(logx+logy)

2

1

(log(xy))=

2

1

(logx+logy)

2

1

(logx+logy)=

2

1

(logx+logy)

LHS=RHS

Answer 2

Answer:

Step-by-step explanation:

Step-by-step explanation:

Given that,

x

2

+y

2

=47xy

Add 2xy both sides,

x

2

+y

2

+2xy=47xy+2xy

(x+y)

2

=49xy

Square root both sides,

x+y=7

xy

Substitute the above equation in,

log(

7

x+y

)=

2

1

(logx+logy)

log(

7

7

xy

)=

2

1

(logx+logy)

log(

7

7(xy)

2

1

)=

2

1

(logx+logy)

log((xy)

2

1

)=

2

1

(logx+logy)

2

1

(log(xy))=

2

1

(logx+logy)

2

1

(logx+logy)=

2

1

(logx+logy)

LHS=RHS

Hope it helped...u dear..